Is there a formal name for this philosophical AI problem?
If something is indistinguishable from a human it is as intelligent as a human. There is no such thing as simulated intelligence. 

Consciousness of course is a different matter and I suspect that's what you really have in mind (no pun intended). 

The question how to distinguish somebody who is truly conscious from somebody who just acts outwardly like a conscious being is often discussed under the term philosophical zombie.